Journal of Applied Probability
- J. Appl. Probab.
- Volume 48, Number 2 (2011), 569-575.
Asymptotic properties of a leader election algorithm
We consider a serialized coin-tossing leader election algorithm that proceeds in rounds until a winner is chosen, or all contestants are eliminated. The analysis allows for either biased or fair coins. We find the exact distribution for the duration of any fixed contestant; asymptotically, it turns out to be a geometric distribution. Rice's method (an analytic technique) shows that the moments of the duration contain oscillations, which we give explicitly for the mean and variance. We also use convergence in the Wasserstein metric space to show that the distribution of the total number of coin flips (among all participants), suitably normalized, approaches a normal limiting random variable.
J. Appl. Probab., Volume 48, Number 2 (2011), 569-575.
First available in Project Euclid: 21 June 2011
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Kalpathy, Ravi; Mahmoud, Hosam M.; Ward, Mark Daniel. Asymptotic properties of a leader election algorithm. J. Appl. Probab. 48 (2011), no. 2, 569--575. doi:10.1239/jap/1308662645. https://projecteuclid.org/euclid.jap/1308662645